What are the divisors of 9617?

1, 59, 163, 9617

There is a total of 4 positive divisors.
The sum of these divisors is 9840.
The arithmetic mean is 2460.

4 odd divisors

1, 59, 163, 9617

How to compute the divisors of 9617?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 9617 by each of the numbers from 1 to 9617 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

9617 / 1 = 9617 (the remainder is 0, so 1 is a divisor of 9617)
9617 / 2 = 4808.5 (the remainder is 1, so 2 is not a divisor of 9617)
9617 / 3 = 3205.6666666667 (the remainder is 2, so 3 is not a divisor of 9617)
...
9617 / 9616 = 1.0001039933444 (the remainder is 1, so 9616 is not a divisor of 9617)
9617 / 9617 = 1 (the remainder is 0, so 9617 is a divisor of 9617)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 9617 (i.e. 98.066304100848). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

9617 / 1 = 9617 (the remainder is 0, so 1 and 9617 are divisors of 9617)
9617 / 2 = 4808.5 (the remainder is 1, so 2 is not a divisor of 9617)
9617 / 3 = 3205.6666666667 (the remainder is 2, so 3 is not a divisor of 9617)
...
9617 / 97 = 99.144329896907 (the remainder is 14, so 97 is not a divisor of 9617)
9617 / 98 = 98.132653061224 (the remainder is 13, so 98 is not a divisor of 9617)